Home
Class 12
MATHS
Matrix A such that A^2=2A-I ,w h e r eI ...

Matrix `A` such that `A^2=2A-I ,w h e r eI` is the identity matrix, the for `ngeq2. A^n` is equal to `2^(n-1)A-(n-1)l` b. `2^(n-1)A-I` c. `n A-(n-1)l` d. `n A-I`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

If I_n is the identity matrix of order n, then rank of I_n is

A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P^(n)=5I-8P , then n is

If A is a nilpotent matrix of index 2, then for any positive integer n ,A(I+A)^n is equal to (a) A^(-1) (b) A (c) A^n (d) I_n

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

Let A=[[0, 1],[ 0, 0]] show that (a I+b A)^n=a^n I+n a^(n-1)b A , where I is the identity matrix of order 2 and n in N .

If A is a non singular square matrix then |adj.A| is equal to (A) |A| (B) |A|^(n-2) (C) |A|^(n-1) (D) |A|^n

If I_n is the identity matrix of order n then (I_n)^-1 (A) does not exist (B) =0 (C) =I_n (D) =nI_n

If A is a square matrix such that A^2=A ,t h e n(I+A)^3-7A is equal to (a) A (b) I-A (c) I (d) 3A

If sum_(r=1)^n r^4=I(n),t h e nsum_(r=1)^n(2r-1)^4 is equal to a. I(2n)-I(n) b. I(2n)-16 I(n) c. I(2n)-8I(n) d. I(2n)-4I(n)

i ^n+i ^(n+1)+i ^(n+2)+i ^(n+3) (n∈N) is equal to